Therefore, fff is periodic with period2⁢π2π2\pi. For expressing the Fourier coefficientsamsubscriptama_{m} and bmsubscriptbmb_{m}
with the function itself, we first multiply the series (1) by cos⁡n⁢xnx\cos{nx} (n∈ℤnℤn\in\mathbb{Z}) and integrate from -ππ-\pi to ππ\pi. Supposing that we can integrate termwise, we may write